Question

A line segment has endpoints at A(-2, 4) and B(-4, 2). Write an equation in slope-intercept form for a line that bisects this segments that is parallel to the line y = -2x + 5. (Hint: You will need to find the midpoint of the segment first so that you know a point that will be on your new line.)
Please enter A and B for your answer in the form: y = Ax + B
A=
B=

Answer 1

The equation of the line that bisects the given segment is y = -2x -3.

The given points coordinates;

A(-2, 4), B(-4, 2)

The mid-point of the given coordinate points;

$Mid-point = \frac{x_1 + x_2 }{2} , \ \frac{y_1 + y_2}{2} \\\\Mid-point = \frac{-2 -4}{2} , \ \frac{4+2}{2} \\\\Mid-point = (-3, 3)$

The slope of the given line is calculated as;

y = -2x + 5

slope = -2

The equation of the line that bisects the given coordinate points;

$\frac{y-y_1}{x-x_1} = -2\\\\\frac{y-3}{x-(-3)} = -2\\\\\frac{y-3}{x+3} = -2\\\\y-3 = -2(x+3)\\\\y-3 = -2x -6\\\\y = -2x -3$

Thus, the equation of the line that bisects the given segment is y = -2x -3.

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